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K.S.Lingamurty, P.Mallikarjuna Rao , T. Sandhya , K.Sri chandan/ International Journal of
Engineering Research and Applications (IJERA)
ISSN: 2248-9622
www.ijera.com
Vol. 1, Issue 2, pp.235-240
Design and Performance Analysis
Analysis of Single Sided
Linear Induction Motor
K.S.Lingamurty, P.Mallikarjuna Rao* , T. Sandhya , K.Sri chandan
ABSTRACT: This paper suggests and describes the
methodology for the design of a linear induction
motor which will accelerate the rotor (Aluminum
sheet) with a specified mass with the required
acceleration to the target distance. The study throws
new light on the fundamental principles of linear
induction. A Single sided linear induction motor
(SLIM) of specified parameters is designed using a
user-interactive MATLAB program. The SLIM
design and performance equations and design
procedures are developed and its performance is
predicted using equivalent circuit models. End effects
and edge effects are neglected in this study.
Optimum design parameters are obtained by the
iterative procedure of the design algorithm by
choosing
various
design
parameters.
The
performance of the SLIM for different values of
thrust, rotor acceleration, rotor thickness and slip
values is analyzed. The effect of variation of such
parameters on the performance of the machine is
discussed.
Keywords- Electrical machine design, Linear motors,
single sided linear induction motor (SLIM),
Equivalent circuit model.
__________________________________________
Dr.K.S.Lingamurty,Professor & HOD, Department of Electrical
and Electronics Engineering, GIT, GITAM University, Andhra
Pradesh, India (email:[email protected])
*corresponding author: Dr. P.Mallikarjuna Rao, Professor, Dept.
of Electrical Engineering, Andhra University, Visakhapatnam,
A.P., India-530003, (email:[email protected])
T.Sandhya. and K.Sri Chandan.
Asst. Professors in the
Department of Electrical and Electronics Engineering, GIT,
GITAM
University,Andhra
Pradesh,
India
(email:
[email protected], [email protected])
I. INTRODUCTION
Linear motors have been around for nearly a
century, and yet are still in their early stages of
development. Because of their large air gaps, low
efficiencies and low power factor they have not been
considered viable design options for many high-speed
linear motion application [1].
Recently linear motors have been getting a
primary look by variety of users that require a
traction force by means of something other than
friction. High speed trains and monorails are just a
few of the recent designs using linear motors.
Conceptually all types of motors can have
possible linear configurations (dc, induction,
synchronous and reluctance). Due to high starting
thrust force, simple structure, alleviation of gear
between motor and the motion devices, reduction of
mechanical losses, high speed operation, low noise,
low cost linear induction motors (LIMs) have been
broadly used in industrial applications like conveyor
systems, material handling and storage, people
movers, liquid metal pumping, accelerators and
launchers, machine tool operation, airport baggage
handling, opening and closing drapes, operation of
sliding doors and low and medium speed trains.
II.SINGLE-SIDED LINEAR INDUCTION
MOTOR (SLIM)
The structure diagram of a single-sided
linear induction motor (SLIM) is shown in Fig. 1.
The SLIM primary can be simply regarded as a rotary
cut-open stator and then rolled flat [1]. The
secondary, similar with the rotary induction motor
(RIM) rotor, often consists of a sheet conductor, such
as copper or aluminum, with a solid back iron acting
235|Page
K.S.Lingamurty, P.Mallikarjuna Rao , T. Sandhya , K.Sri chandan/ International Journal of
Engineering Research and Applications (IJERA)
ISSN: 2248-9622
www.ijera.com
Vol. 1, Issue 2, pp.235-240
as the return path for the magnetic flux. The thrust
corresponding to the RIM torque can be produced by
the reaction between the air-gap flux density and the
eddy current in the secondary sheet.
Where R is the stator radius of the rotary induction
motor.
It is important to note that the linear speed does not
depend upon the number of poles but only on the pole
pitch. The parameter τ is the distance between two
neighboring poles on the circumference of the stator,
called pole pitch. The stator circumference of the
rotary induction motor, 2πR, in Eqn.(3) is equal to the
length of the SLIM stator core, Ls. Therefore the pole
pitch of a LIM is defined as
τ=
Fig1. Single-sided LIM
The stator produces a sinusoidally
distributed magnetic field in the air-gap rotating at
the uniform speed 2ω/p, with ω representing the
network pulsation (related to the frequency f by ω=
2πf) and p the number of poles [2]. The relative
motion between the rotor conductors and the
magnetic field induces a voltage in the rotor. This
induced voltage will cause a current to flow in the
rotor and will generate a magnetic field. The
interaction of these two magnetic fields will produce
a torque that drags the rotor in the direction of the
field. Slip is the relative motion needed in the
induction motor to induce a voltage in the rotor, if
the velocity of the rotor is Vr , then the slip of LIM/
SLIM can be denoted as,
S=
VS − Vr
VS
2ω R
= 2 fτ
p
…. (3)
The analysis and design of a low-speed flat SLIM can
be done by the use of an approximate equivalent
circuit that is developed. To determine the parameters
of the circuit, the design formulas of the rotary
induction motor for the given application will be
attributed to the SLIM. As it is well known that often
the secondary of a SLIM is made of a conducting
sheet. The concept of surface resistivity is very useful
in finding the resistance of such a secondary.
III . EQUIVALENT CIRCUIT MODEL
The approximate equivalent circuit [5] of a LIM is
presented as shown in Fig. 2.
This circuit is on a per phase basis.
… (1)
Where Vs is the synchronous velocity , is the same as
that of the rotary induction motor, given by
V s=
2Π R Ls
=
p
p
…(2)
Fig. 2. Approximate equivalent circuit of LIM
A. Per-phase stator resistance ( R1 ) :
This is the resistance of each phase of the LIM stator
windings. R1 is calculated from
R1 = ρ w
lw
A wt
…(4)
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K.S.Lingamurty, P.Mallikarjuna Rao , T. Sandhya , K.Sri chandan/ International Journal of
Engineering Research and Applications (IJERA)
ISSN: 2248-9622
www.ijera.com
Vol. 1, Issue 2, pp.235-240
where,
ρw
is the volume resistivity of the copper
lw is the length of
the copper wire per phase, and A wt is the crosswire used in the stator winding,
sectional area of the wire.
The length of the copper wires
kw is the winding factor , g e is the equivalent
air gap given by and Wse is the equivalent stator
where
width
D. Per-phase rotor resistance ( R2 ) :
lw is calculated from
lw = N1lwl
The per-phase rotor resistance
slip, as shown in Fig. 2.
… (5)
Where lwl = mean length of one turn of the stator
winding per phase
B. Per-phase stator-slot leakage reactance( X1 ) :
The flux that is produced in the stator windings is not
completely linked with the rotor conductors. There
will be some leakage flux in the stator slots and hence
stator-slot leakage reactance X1. This leakage flux is
generated from an individual coil inside a stator slot
and caused by the slot openings of the stator iron
core. In a LIM stator having open rectangular slots
with a double-layer winding, X1 can be determined
from
R2 can be calculated from
the goodness factor G and the per-phase magnetizing
reactance X m as
R2 =
Xm
G
…(8)
where the goodness factor is defined as
G=
Where
 

W
3
2 µoπ f  λs  1 +  + λd  s + λe I ce  N12
p
 q1
 

X1 =
p
R2 is a function of
ρr
2µo f τ 2
ρ 
π  r  ge
 d 
… (9)
is the volume resistivity of the rotor
conductor outer layer, which is aluminum here.
…(6)
IV. PERFORMANCE CALCULATION
Where Ws=stator width, lce =length of end conductor
wire , N1 = Turns per phase , q1 =slots per pole per
phase .
C. Per-phase magnetizing reactance ( X m ):
The per-phase magnetizing reactance,
X m [4] ,
The procedure of performance analysis based on the
equivalent circuit shown in Fig. 2, where the
magnitude of the rotor phase current I2 [6] can be
calculated from
I2 =
is shown in Fig.8
Xm =
24 µoπ fWse kw N12 r
π 2 pg e
… (10)
I1
1
(SG )
… (7)
2
+1
The LIM electromagnetic thrust [Fs] becomes
Fs =
m I 12 R 2

1

 ( S G
)
2
…
(11)

+ 1 V s S

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K.S.Lingamurty, P.Mallikarjuna Rao , T. Sandhya , K.Sri chandan/ International Journal of
Engineering Research and Applications (IJERA)
ISSN: 2248-9622
www.ijera.com
Vol. 1, Issue 2, pp.235-240
9000
S=0.1
8000
S=0.05
7000
6000
Thrust (N)
5000
4000
3000
2000
1000
0
0
5
10
15
Rotor Velocity, Vr, (m/sec)
20
25
Fig 3. Thrust versus Rotor Velocity of SLIM with change in slip
4
2.5
x 10
d=0.3
2
Thrust (N)
1.5
1
d=0.03
0.5
0
0
5
10
15
Rotor Velocity Vr (m/sec)
20
25
Fig 4. Thrust versus Rotor Velocity of SLIM for Aluminum thickness
9000
8000
7000
Thrust (N)
6000
5000
4000
p=4
3000
p=2
2000
1000
0
0
5
10
15
Rotor Velocity, Vr (m/sec)
20
25
Fig 5. Thrust versus Rotor Velocity of SLIM for No. of poles
238|Page
K.S.Lingamurty, P.Mallikarjuna Rao , T. Sandhya , K.Sri chandan/ International Journal of
Engineering Research and Applications (IJERA)
ISSN: 2248-9622
www.ijera.com
Vol. 1, Issue 2, pp.235-240
The LIM input active power is the summation of the
output power and the copper losses from the stator
and rotor,
Pi = Po + mI12 R1 + mI 22 R2
Where,
… (12)
Po =output power given by
Po = mI 22
R2
 1− S 
− mI 22 R2 = mI 22 R2 
 .. (13)
S
 S 
mI12 R1 , mI 22 R2 = stator & rotor copper loss.
The efficiency of the LIM is found by
η=
Po
Pi
… (14)
V. RESULTS
The input data used for SLIM design in
MATLAB program was given in appendix along
with the slot geometry .The output results at rated
slips of 5% and 10% are tabulated below .
Description
Pole pitch , τ ( (m)
Slot pitch , (m)
Stator length ,Ls(m)
"Target" thrust (N)
Slot width , ws(m)
Tooth width ,wt (m)
Slot depth , hs (m)
Actual thrust at specified
Vr (N)
Stator efficiency , η
5 %slip
0.2105
0.035
0.8421
4905
0.0205
0.0145
0.01101
6026.44
10% slip
0.2222
0.037
0.8889
4905
0.02419
0.0128
0.0112
6028.1
94.98
89.98 %
Rated stator Current , I1(A)
Rotor Phase current I2 (A)
348.02
288.23
512.64
491.46
The performance characteristics of the SLIM,
thrust Fs as a function of rotor velocity Vr , at
different slips of 5% and 10% are shown in Fig.3,
for different rotor aluminum thickness of 0.03m and
0.3m are shown in Fig.4 and for change in number of
poles for p=2 & 4 are shown in Fig.5.
VI . CONCLUSION
In this research article, the equivalent
circuit has been derived to analyze the performance
of the short-secondary SLIM. It can be concluded
that the slip, the thickness of rotor aluminum outer
layer, number of poles plays a very important role in
the performance of the SLIM. As the slip of the
machine increases thrust of the machine decreases.
Also when the thickness of the aluminum sheet is
increased thrust increases. Hence, care should be
taken in choosing the best value for aluminum
thickness which yields maximum thrust at a required
efficiency. Further , increase in the number of poles,
results in increase in the thrust. So, from the
parametric analysis it can be concluded that the input
parameters like the slip, thickness of aluminum sheet
and number of poles play a vital role in the
performance parameters, thrust and efficiency. Based
on the target values of rotor velocity and thrust, these
parameters should be chosen which gives the best
possible thrust closest to the target value at a required
efficiency. The results show that the proposed
equivalent circuit gives more accurate solutions and
can be used as an effective tool to determine the
performances of such type of motor.
REFERENCES
1. A complete equivalent circuit of a linear induction motor with
sheet secondary Pai, R.M.; Boldea, I.; Nasar, S.A.; Magnetics,
IEEE Transactions on , Volume:24 , Issue: 1 , Jan. 1988 Pages:639
– 654
2. The causes and consequences of phase unbalance in single-sided
linear induction motors Adamiak, K.; Ananthasivam, K.; Dawson,
G.E.; Eastham, A.R.; Gieras,J.F.; Magnetics, IEEE Transactions
on , Volume: 24 , Issue: 6 , Nov 1988 Pages:3223 – 3233.
3. Obtaining the operating characteristics of linear induction
motors: a new approach Mirsalim, M.; Doroudi, A.; Moghani, J.S.;
Magnetics, IEEE Transactions on, Volume: 38, Issue: 2, March
2002 Pages: 1365 – 1370.
4. Optimum Design of Single-Sided Linear Induction Motors for
Improved Motor Performance Bazghaleh, A.Z. ; Naghashan, M.R.
; Meshkatoddini, M.R. ; Power & Water Univ. of Technol.,
Tehran, Iran Magnetics, IEEE Transactions on Issue Date : Nov.
2010 Volume : 46 , Issue:11 On page(s): 3939 ISSN : 00189464.
5. An Improved Equivalent Circuit Model of a Single-Sided Linear
Induction Motor. Wei Xu Jian Guo Zhu Yongchang Zhang Yaohua
239|Page
K.S.Lingamurty, P.Mallikarjuna Rao , T. Sandhya , K.Sri chandan/ International Journal of
Engineering Research and Applications (IJERA)
ISSN: 2248-9622
www.ijera.com
Vol. 1, Issue 2, pp.235-240
Li Yi Wang Youguang Guo Univ. of Technol. Sydney, Sydney,
NSW, Australia. IEEE Transactions on Issue Date : Jun 2010
Volume : 59 , Issue:5 On page(s): 2277 ISSN : 0018-9545
6. Equivalent circuits for single-sided linear induction motors . Wei
Xu Jianguo Zhu Youguang Guo Yi Wang Yongchang Zhang
Longcheng Tan Sch. of Electr., Mech. & Mechatron. Syst., Univ.
of Technol. Sydney, Sydney, NSW, Australia , Energy Conversion
Congress and Exposition, 2009. ECCE 2009. IEEE
Issue Date :
20-24 Sept. 2009 On page(s): 1288
Print ISBN: 978-1-4244-2893-9
APPENDIX
Specifications of SLIM
Aluminum thickness, d (in meters) = 0.03
Number of phases, m = 3
Primary line to line voltage(V) = 440
Supply frequency, f (Hz) = 50
Number of poles , p= 4
Number of slots per pole per phase, N1 = 2
Rated slip, S = 0.1
Width of the stator,Ws(m) = 0.02
Acceleration due to gravity, g (m/sec2) =50
Weight of the rotor ,m (kg) =10
Rated rotor velocity, Vr (m/sec) = 20
Fig. 6 .SLIM geometry
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